Nonlinear metric mean dimension
Abstract
Motivated by the nonlinear thermodynamic formalism introduced by Buzzi, Klonecker, and Leplaideur [5], we define the nonlinear metric mean dimension, designed to capture refined complexity beyond the reach of topological pressure. Our approach is explicitly convex-analytic: We formulate the nonlinear pressure and its scaled counterparts as convex, monotone, translation-equivariant functionals on spaces of energies, and we derive two variational principles via standard tools from convex analysis. Within this framework, we also establish existence results for nonlinear equilibrium measures and present examples illustrating the scope and limitations of the theory.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
advanced mathematical theories
Statistical Mechanics and Entropy
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems - S
- Volume
- 30
- Issue
- 0
- Pages
- 345–369
- Publication date
- 1 January 2026
- Language
- EN